Each of the 320 nanobots is a point-mass agent obeying overdamped feedback dynamics — the same control law used in real swarm-robotics shape formation and DNA-origami-style directed self-assembly:
v_i = k·(target_i − x_i) feedback toward assigned target
+ Σ_j repel(x_i − x_j) local pairwise repulsion (j within radius r)
+ √(2D)·ξ(t) thermal (Brownian) noise, ξ ~ N(0,1)
x_i(t+dt) = x_i(t) + v_i·dt
Every agent is assigned the nearest unclaimed slot on the target surface (a greedy nearest-neighbor match, computed once per shape) — there is no central controller broadcasting positions; each nanobot only reacts to its own target offset and its nearby neighbors, exactly the distributed feedback-loop architecture described for self-organizing nanoscale systems.
- Gain k — how strongly each agent is pulled toward its target; low k makes assembly slow and wobbly, high k makes it snap into place.
- Thermal noise D — random jitter representing molecular-scale thermal agitation; too much noise and the swarm never settles, exactly as real self-assembly requires low enough thermal energy relative to the binding potential.
- Repulsion — a short-range 1/r² push that keeps agents from overlapping, so the shape forms as a hollow shell rather than collapsing to a point.
- Disrupt swarm — randomizes every position, then lets the same local feedback law re-converge the swarm with zero re-programming — a demonstration of the self-healing property that makes distributed control attractive for real nanoscale systems (damage or perturbation is corrected locally, not by a central planner).
RMS error is the root-mean-square distance of all agents from their assigned target slot (the Lyapunov-like quantity the feedback law drives toward zero); coherence is the fraction of agents within 0.12 units of their target — a proxy for "how assembled" the structure currently is.